Question: Solve for $x$ and $y$ using elimination. ${3x-2y = -7}$ ${-4x-5y = -52}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $5$ and the bottom equation by $-2$ ${15x-10y = -35}$ $8x+10y = 104$ Add the top and bottom equations together. $23x = 69$ $\dfrac{23x}{{23}} = \dfrac{69}{{23}}$ ${x = 3}$ Now that you know ${x = 3}$ , plug it back into $\thinspace {3x-2y = -7}\thinspace$ to find $y$ ${3}{(3)}{ - 2y = -7}$ $9-2y = -7$ $9{-9} - 2y = -7{-9}$ $-2y = -16$ $\dfrac{-2y}{{-2}} = \dfrac{-16}{{-2}}$ ${y = 8}$ You can also plug ${x = 3}$ into $\thinspace {-4x-5y = -52}\thinspace$ and get the same answer for $y$ : ${-4}{(3)}{ - 5y = -52}$ ${y = 8}$